MinT - Best Known (68, 68+64, s)-Nets in Base 9

Best Known (68, 68+64, s)-Nets in Base 9

(68, 68+64, 232)-Net over F₉ — Constructive and digital

Digital (68, 132, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 66, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(68, 68+64, 284)-Net over F₉ — Digital

Digital (68, 132, 284)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+64, 13785)-Net in Base 9 — Upper bound on s

There is no (68, 132, 13786)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912784 247839 179167 203227 879204 287362 264954 158548 032849 816964 584643 245925 534852 058308 269727 909982 399001 405282 417684 417711 169025 > 9¹³² [i]